Fingerprint recognition is widely used for verification and identification in many commercial, governmental and forensic applications. The orientation field (OF) plays an important role at various processing stages in fingerprint recognition systems. OFs are used for image enhancement, fingerprint alignment, for fingerprint liveness detection, fingerprint alteration detection and fingerprint matching. In this study, a novel approach is presented to globally model an OF combined with locally adaptive methods. The authors show that this model adapts perfectly to the ‘true OF’ in the limit. This perfect OF is described by a small number of parameters with straightforward geometric interpretation. Applications are manifold: Quick expert marking of very poor quality (for instance latent) OFs, high-fidelity low parameter OF compression and a direct road to ground truth OFs markings for large databases, say. In this contribution, they describe an algorithm to perfectly estimate OF parameters automatically or semi-automatically, depending on image quality, and they establish the main underlying claim of high-fidelity low parameter OF compression.